Does activating auto dependencies have an adverse effect on server or database resources?

It is a double-edged sword... it won't hurt from a performance perspective, but on an administrative side it can cause some dependencies you do not want, and you need to some manual work again.

if you have tested it in your lab and i worked as expected and no "unwanted" dependencies came up, you can switch it on in Prod

Thanks for the reply! ...  it's very much appreciated.  We didn't see any unwanted dependencies in our testing, but I do expect we'll get a few.  I wish I could turn on auto dependencies on a site by site basis, but it appears to be all or nothing.  If turned on, I can deactivate past that..   

Again, thank you!

you are correct, it is a global setting - all or nothing

Technical "yes", realistically I dont expect you'd notice a difference 

It's both important but also animplied TLC sort of scenario